The first method is the same as in [1]}, and can also be described within a more general framework of convex geometric Demazure operators [2]}.
Namely, we consider a (possibly virtual) polytope \(P\subset \mathbb {R}^n\)  obtained as
\(P=D_{i_1}D_{i_2}\ldots D_{i_\ell }(p),\) 
